A functional dataset where the individual functions are given by: \(y_i(t) = z_{i,1} e^{-(t-1.5)^2/2} + z_{i,2}e^{-(t+1.5)^2/2}\), \(t \in [-3, 3], ~i=1,2,\dots, 21\), where \(z_{i,1}\) and \(z_{i,2}\) are i.i.d. normal with mean one and standard deviation 0.25. Each of these functions is then warped according to: \(\gamma_i(t) = 6({e^{a_i(t+3)/6} -1 \over e^{a_i} - 1}) - 3\) if \(a_i \neq 0\), otherwise \(\gamma_i = \gamma_{id}\) (\(gamma_{id}(t) = t\)) is the identity warping). The variables are as follows: f containing the 21 functions of 101 samples and time which describes the sampling which has been aligned.
simu_warp_mediansimu_warp_median
A list which contains the output of the time_warping() function finding the
median applied on the data set simu_data.